多項式相位信號的檢測和參數估計
發(fā)布時間：2018-11-22 10:14
【摘要】：多項式相位信號廣泛應用于雷達、聲吶、無線通信和地震學等領域,對此,對多項式相位信號的檢測和參數估計是一個具有重要理論意義和重要應用價值的研究方向。另一方面,噪聲在物質世界無處不在,多項式相位信號往往淹沒在噪聲中,因此,減少多項式相位信號的檢測和參數估計的信噪比門限成為許多研究者努力的一個目標。對多項式相位信號的檢測和參數估計算法,大致可分為兩類,一類是多線性變換,比如高階模糊函數和它的乘積版本--乘積高階模糊函數;另一類是相位展開的方式,比如Kitchen’s的相位展開估計算法和Djuric的估計算法。這兩類算法都有它們的優(yōu)點和缺點。在過去二十年里,對于單分量多項式相位信號的檢測和參數估計,提出了許多理論和方法,然而這些理論和方法對于處理多分量多項式相位信號有著限制和缺陷,主要是多分量多項式相位信號的處理比單分量復雜得多,因此,結合已有的對多項式相位信號的處理方法,本文展開了如下方面的創(chuàng)新性研究:1、采用稀疏分解對加性高斯白噪聲中多項式相位信號進行檢測和參數估計。系統研究了在加性高斯白噪聲條件下,采用稀疏分解實現對多項式相位信號的最優(yōu)檢測,并結合快速傅里葉變換,提出一種針對多項式相位信號的快速稀疏分解算法,該算法大大降低了參數估計的信噪比門限2、結合字典學習算法和稀疏表示實現對加性高斯白噪聲中多項式相位信號的去噪。提出一種能去除多項式相位信號噪聲的字典學習算法,用這種算法得到的字典,采用稀疏表示,能有效地提高信噪比。3、分析并解決了乘積三次相位函數與高階模糊函數(Product Cubic Phase Function and High-order Ambiguity Function,PCPF-HAF)算法在多分量多項式相位信號參數估計中存在的不確定性問題。分析了PCPF-HAF算法在估計多分量多項式相位信號參數的存在的不確定性問題,對于這個問題,提出了兩種有效的解決方法,一種采用設定三個時間點的方式,這種方法主要根據分量在三個時間點上所求的頻率在同一條直線上;第二種方法采用兩個時間點的方式,對于各種可能的最高兩階的相位參數組成的多項式相位信號,把它們與變換后的信號相乘并求和,則求和最大值所對應的參數估計就是正確的參數估計。4、提出了基于PCPF-HAF的優(yōu)化多分量多項式相位信號參數估計算法為了PCPF-HAF算法能用快速傅里葉變換,提出利用非一致間隔采樣方法,并針對多分量的三階多項式相位信號不能使用多個滯后時間達到相乘的目的,提出采用多個比例因子來達到相乘的目的。在提出的優(yōu)化算法中,針對濾波/相位展開的改進參數估計算法沒有實現對幅值參數的改進,提出采用奇異值分解的方法改進幅值參數的估計。
[Abstract]:Polynomial phase signals are widely used in radar, sonar, wireless communication and seismology. Therefore, the detection and parameter estimation of polynomial phase signals have important theoretical significance and important application value. On the other hand, noise is ubiquitous in the material world and polynomial phase signals are often submerged in noise. Therefore, reducing the signal-to-noise ratio (SNR) threshold of polynomial phase signal detection and parameter estimation has become a goal of many researchers. The detection and parameter estimation algorithms of polynomial phase signal can be divided into two categories: one is multi-linear transformation, such as high-order fuzzy function and its product version-product high-order fuzzy function; The other is phase unwrapping, such as Kitchen's 's phase unwrapping estimation algorithm and Djuric's estimation algorithm. Both algorithms have their advantages and disadvantages. In the past two decades, many theories and methods have been proposed for the detection and parameter estimation of single-component polynomial phase signals. However, these theories and methods have limitations and defects in the processing of multi-component polynomial phase signals. The processing of multi-component polynomial phase signal is much more complicated than that of single component. Therefore, combining with the existing processing methods of polynomial phase signal, the following innovative researches are carried out in this paper: 1. Sparse decomposition is used to detect and estimate polynomial phase signals in additive Gao Si white noise. Under the condition of additive Gao Si white noise, the optimal detection of polynomial phase signal is realized by sparse decomposition, and a fast sparse decomposition algorithm for polynomial phase signal is proposed in combination with fast Fourier transform (FFT). This algorithm greatly reduces the SNR threshold of parameter estimation by 2, and combines dictionary learning algorithm and sparse representation to realize the denoising of polynomial phase signals in additive Gao Si white noise. This paper presents a dictionary learning algorithm which can remove the noise of polynomial phase signal. The dictionary obtained by this algorithm can effectively improve the signal-to-noise ratio (SNR) by using sparse representation. The uncertainty of product cubic phase function and high-order ambiguity function (Product Cubic Phase Function and High-order Ambiguity Function,PCPF-HAF algorithm in multi-component polynomial phase signal estimation is analyzed and solved. This paper analyzes the uncertainty of PCPF-HAF algorithm in estimating the parameters of multi-component polynomial phase signal. For this problem, two effective solutions are proposed, one is to set three time points, and the other is to solve the problem. This method is mainly based on the frequency of the component at three time points in the same line. In the second method, the polynomial phase signals composed of the highest two order phase parameters are multiplied and summed by the transformed signals in two time points. Then the parameter estimation corresponding to the summation maximum value is the correct parameter estimation. 4. An optimized multi-component polynomial phase signal parameter estimation algorithm based on PCPF-HAF is proposed so that the PCPF-HAF algorithm can use fast Fourier transform. A non-uniform interval sampling method is proposed. In view of the fact that multi-component third-order polynomial phase signals can not be multiplied by multiple delay time, multiple scale factors are proposed to multiply each other. In the proposed optimization algorithm, the improved filtering / phase unwrapping parameter estimation algorithm has not realized the improvement of the amplitude parameter, so the singular value decomposition method is proposed to improve the amplitude parameter estimation.
【學位授予單位】：重慶大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TN911.23
本文編號：2348998
[Abstract]:Polynomial phase signals are widely used in radar, sonar, wireless communication and seismology. Therefore, the detection and parameter estimation of polynomial phase signals have important theoretical significance and important application value. On the other hand, noise is ubiquitous in the material world and polynomial phase signals are often submerged in noise. Therefore, reducing the signal-to-noise ratio (SNR) threshold of polynomial phase signal detection and parameter estimation has become a goal of many researchers. The detection and parameter estimation algorithms of polynomial phase signal can be divided into two categories: one is multi-linear transformation, such as high-order fuzzy function and its product version-product high-order fuzzy function; The other is phase unwrapping, such as Kitchen's 's phase unwrapping estimation algorithm and Djuric's estimation algorithm. Both algorithms have their advantages and disadvantages. In the past two decades, many theories and methods have been proposed for the detection and parameter estimation of single-component polynomial phase signals. However, these theories and methods have limitations and defects in the processing of multi-component polynomial phase signals. The processing of multi-component polynomial phase signal is much more complicated than that of single component. Therefore, combining with the existing processing methods of polynomial phase signal, the following innovative researches are carried out in this paper: 1. Sparse decomposition is used to detect and estimate polynomial phase signals in additive Gao Si white noise. Under the condition of additive Gao Si white noise, the optimal detection of polynomial phase signal is realized by sparse decomposition, and a fast sparse decomposition algorithm for polynomial phase signal is proposed in combination with fast Fourier transform (FFT). This algorithm greatly reduces the SNR threshold of parameter estimation by 2, and combines dictionary learning algorithm and sparse representation to realize the denoising of polynomial phase signals in additive Gao Si white noise. This paper presents a dictionary learning algorithm which can remove the noise of polynomial phase signal. The dictionary obtained by this algorithm can effectively improve the signal-to-noise ratio (SNR) by using sparse representation. The uncertainty of product cubic phase function and high-order ambiguity function (Product Cubic Phase Function and High-order Ambiguity Function,PCPF-HAF algorithm in multi-component polynomial phase signal estimation is analyzed and solved. This paper analyzes the uncertainty of PCPF-HAF algorithm in estimating the parameters of multi-component polynomial phase signal. For this problem, two effective solutions are proposed, one is to set three time points, and the other is to solve the problem. This method is mainly based on the frequency of the component at three time points in the same line. In the second method, the polynomial phase signals composed of the highest two order phase parameters are multiplied and summed by the transformed signals in two time points. Then the parameter estimation corresponding to the summation maximum value is the correct parameter estimation. 4. An optimized multi-component polynomial phase signal parameter estimation algorithm based on PCPF-HAF is proposed so that the PCPF-HAF algorithm can use fast Fourier transform. A non-uniform interval sampling method is proposed. In view of the fact that multi-component third-order polynomial phase signals can not be multiplied by multiple delay time, multiple scale factors are proposed to multiply each other. In the proposed optimization algorithm, the improved filtering / phase unwrapping parameter estimation algorithm has not realized the improvement of the amplitude parameter, so the singular value decomposition method is proposed to improve the amplitude parameter estimation.
【學位授予單位】：重慶大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TN911.23
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